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The meromorphic functional calculus developed in Part I overcomes thenondiagonalizability of linear operators that arises often in the temporalevolution of complex systems and is generic to the metadynamics of predictingtheir behavior. Using the resulting spectral decomposition, we deriveclosed-form expressions for correlation functions, finite-length Shannonentropy-rate approximates, asymptotic entropy rate, excess entropy, transientinformation, transient and asymptotic state uncertainty, and synchronizationinformation of stochastic processes generated by finite-state hidden Markovmodels. This introduces analytical tractability to investigating informationprocessing in discrete-event stochastic processes, symbolic dynamics, andchaotic dynamical systems. Comparisons reveal mathematical similarities betweencomplexity measures originally thought to capture distinct informational andcomputational properties. We also introduce a new kind of spectral analysis viacoronal spectrograms and the frequency-dependent spectra of past-future mutualinformation. We analyze a number of examples to illustrate the methods,emphasizing processes with multivariate dependencies beyond pairwisecorrelation. An appendix presents spectral decomposition calculations for oneexample in full detail.

Spectral Simplicity of Apparent Complexity, Part II: Exact Complexities and Complexity Spectra